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I need a program that can give me all the subgroups of a group that I define. I also need it to give me the names of the subgroups as per some predefined library.

I tried GAP. It gives me the subgroups, but each subgroup is represented by a list of generators. There seems to be no way to make it print a name for the subgroups, like say S4 for symmetric group of four elements.

In fact, if I give the generators of S4 as input, it cannot identify it and give an output stating that it is S4.

Any suggestions?

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# Program to find subgroups

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